ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 0 to 40 of 3000e^{0.04t}

解

\int_{0}^{40} 3000 e^{0.04 t} d t

解

296477.43182 \dots

解答ステップ

\int_{0}^{40} 3000 e^{0.04 t} d t

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3000 \cdot \int_{0}^{40} e^{0.04 t} d t

u置換積分法を適用する

= 3000 \cdot \int_{0}^{1.6} e^{u} \frac{1}{0.04} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3000 \cdot \frac{1}{0.04} \cdot \int_{0}^{1.6} e^{u} d u

簡素化

= 3000 \cdot 25 \cdot \int_{0}^{1.6} e^{u} d u

共通積分を使用する:

\int e^{u} d u = e^{u}

= 3000 \cdot 25 [e^{u}]_{0}^{1.6}

簡素化

= 75000 [e^{u}]_{0}^{1.6}

限度を計算する:

3.95303 \dots

= 75000 \cdot 3.95303 \dots

簡素化

= 296477.43182 \dots

グラフ

人気の例

integral from-5 to 4 of (-x^2-3x)

\int_{- 5}^{4} (- x^{2} - 3 x) d x

integral from 1 to 4 of 4/(x^3)

\int_{1}^{4} \frac{4}{x ^{3}} d x

integral from 0 to pi of e^{-x}

\int_{0}^{π} e^{- x} d x

integral from 2 to sqrt(x of)cos(x)

\int_{2}^{x} cos (x) d x

integral from 5x to x^3 of e^{-t^2}

\int_{5 x}^{x^{3}} e^{- t^{2}} d t